Subgroups — C₅×#68167 #14281680

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#4833	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4685	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1478	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	2	1	no	—
11	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
13	C₄×C₅×#67	—	2	1	no	—
14	C₅×#893	C₄	1	1	yes	characteristic
15	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
16	C₅×#67⋊C₄	—	2	1	no	—
17	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
23	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
24	C₅×Dic₃⋊C₈	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	#68167	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₄×C₅×D₄	—	3	1	no	—
30	C₅×#431	—	3	1	no	—
31	C₅×#431	—	3	1	no	—
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₅×D₄⋊C₈	—	3	1	no	—
35	C₅×D₄⋊C₈	D₃	1	1	yes	characteristic, complemented
36	C₂³×C₅×D₃	—	2	1	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂×C₅×#67	—	2	1	no	—
40	C₂²×C₅×Dic₃	—	2	1	no	—
41	C₅×D₃×D₄	—	2	2	no	—
42	C₅×D₃×D₄	C₈	1	4	yes	complemented
43	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	—	2	1	no	—
45	C₂×C₄×C₅×D₃	—	2	1	no	—
46	C₂×C₄×C₅×D₃	—	2	1	no	—
47	C₂×C₄×C₅×D₃	—	4	2	no	—
48	C₂×C₄×C₅×D₃	—	4	2	no	—
49	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₅×#217	—	2	1	no	—
58	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
59	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
60	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₅×Dic₃⋊C₄	—	2	1	no	—
62	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
64	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
65	C₂×C₅×C₃⋊C₈	—	2	1	no	—
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
68	#4833	C₂×C₅	1	1	yes	characteristic, complemented
69	#4685	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
71	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
72	#4483	C₂×C₅	1	1	yes	characteristic, complemented
73	#4459	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₄	—	3	1	no	—
75	C₂³×C₄×C₅	—	6	1	no	—
76	C₄×C₅×D₄	—	3	1	no	—
77	C₄×C₅×D₄	—	3	1	no	—
78	C₄×C₅×D₄	—	3	1	no	—
79	C₄×C₅×D₄	—	6	1	no	—
80	C₄×C₅×D₄	—	6	1	no	—
81	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	—	3	1	no	—
83	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₅×C₄⋊C₈	—	3	1	no	—
86	C₅×C₄⋊C₈	—	6	1	no	—
87	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
88	C₅×C₂²⋊C₈	—	6	1	no	—
89	C₅×C₂²⋊C₈	—	6	1	no	—
90	C₄×C₅×C₈	—	3	1	no	—
91	C₄×C₅×C₈	—	6	1	no	—
92	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
93	#1478	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	1	no	—
95	C₂²×C₅×D₃	—	2	1	no	—
96	C₂²×C₅×D₃	—	2	4	no	—
97	C₂²×C₅×D₃	—	4	2	no	—
98	C₂²×C₅×D₃	—	4	2	no	—
99	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₃×C₅×D₄	—	2	1	no	—
101	C₃×C₅×D₄	C₂×C₈	1	2	yes	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₅×#67	—	2	4	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	4	2	no	—
111	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₅×D₁₂	—	2	1	no	—
115	C₅×D₁₂	C₂×C₈	1	2	yes	—
116	C₄×C₅×D₃	—	2	1	no	—
117	C₄×C₅×D₃	—	2	1	no	—
118	C₄×C₅×D₃	—	4	1	no	—
119	C₄×C₅×D₃	—	4	2	no	—
120	C₄×C₅×D₃	—	4	2	no	—
121	C₄×C₅×D₃	—	4	1	no	—
122	C₄×C₅×D₃	—	4	1	no	—
123	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
124	C₄×C₅×D₃	M₁₆	1	2	yes	—
125	C₃×C₅×C₈	—	4	1	no	—
126	C₃×C₅×C₈	—	4	1	no	—
127	C₅×C₃⋊C₈	—	4	1	no	—
128	C₅×C₃⋊C₈	—	4	1	no	—
129	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
130	C₂²×C₄×D₃	—	2	1	no	—
131	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
132	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic
133	C₄×#67	—	2	1	no	—
134	#893	C₄×C₅	1	1	yes	characteristic
135	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
136	#67⋊C₄	—	2	1	no	—
137	D₃×C₂²⋊C₄	—	2	1	no	—
138	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
139	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
140	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
142	(C₂×D₃)⋊C₈	—	2	1	no	—
143	(C₂×D₃)⋊C₈	—	2	1	no	—
144	Dic₃⋊C₈	—	2	1	no	—
145	C₈×Dic₃	—	2	1	no	—
146	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
147	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₂⁴×C₅	—	6	1	no	—
149	C₂×C₅×D₄	—	3	4	no	—
150	C₂×C₅×D₄	—	3	1	no	—
151	C₂×C₅×D₄	—	6	2	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	3	1	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	6	1	no	—
159	C₂²×C₄×C₅	—	6	1	no	—
160	C₂²×C₄×C₅	—	6	1	no	—
161	C₂²×C₄×C₅	—	6	1	no	—
162	C₂²×C₄×C₅	—	12	2	no	—
163	C₂²×C₄×C₅	—	12	2	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	6	1	no	—
167	C₂×C₅×C₈	—	6	1	no	—
168	C₅×C₄⋊C₄	—	3	1	no	—
169	C₅×C₄⋊C₄	—	6	1	no	—
170	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	6	1	no	—
173	C₅×C₂²⋊C₄	—	6	1	no	—
174	C₅×C₂²⋊C₄	—	6	1	no	—
175	C₄²×C₅	—	3	1	no	—
176	C₄²×C₅	—	3	1	no	—
177	C₄²×C₅	—	3	1	no	—
178	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₄×D₄	—	3	1	no	—
180	#431	—	3	1	no	—
181	#431	—	3	1	no	—
182	D₄⋊C₈	—	3	1	no	—
183	D₄⋊C₈	—	3	1	no	—
184	D₄⋊C₈	—	3	1	no	—
185	D₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	4	1	no	—
188	C₂²×C₃×C₅	—	4	1	no	—
189	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₅×D₃	—	2	1	no	—
191	C₂×C₅×D₃	—	2	1	no	—
192	C₂×C₅×D₃	—	2	2	no	—
193	C₂×C₅×D₃	—	4	8	no	—
194	C₂×C₅×D₃	—	4	1	no	—
195	C₂×C₅×D₃	—	4	1	no	—
196	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
197	C₃×C₄×C₅	—	2	1	no	—
198	C₃×C₄×C₅	—	4	1	no	—
199	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
201	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₅×Dic₃	—	2	1	no	—
204	C₅×Dic₃	—	2	1	no	—
205	C₅×Dic₃	—	4	1	no	—
206	C₅×Dic₃	C₂²⋊C₈	1	2	yes	—
207	C₂³×D₃	—	2	1	no	—
208	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂×#67	—	2	1	no	—
211	C₂²×Dic₃	—	2	1	no	—
212	D₃×D₄	—	2	2	no	—
213	D₃×D₄	C₅×C₈	1	4	yes	complemented
214	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂×C₄×D₃	—	2	1	no	—
216	C₂×C₄×D₃	—	2	1	no	—
217	C₂×C₄×D₃	—	2	1	no	—
218	C₂×C₄×D₃	—	4	2	no	—
219	C₂×C₄×D₃	—	4	2	no	—
220	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
222	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
223	C₂×C₃×C₈	—	2	1	no	—
224	C₂×C₃×C₈	—	2	1	no	—
225	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
226	C₃×C₂²⋊C₄	—	2	1	no	—
227	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
228	#217	—	2	1	no	—
229	(C₂×D₃)⋊C₄	—	2	1	no	—
230	(C₂×D₃)⋊C₄	—	2	1	no	—
231	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
232	Dic₃⋊C₄	—	2	1	no	—
233	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
234	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
235	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
236	C₂×C₃⋊C₈	—	2	1	no	—
237	C₂×C₃⋊C₈	—	2	1	no	—
238	C₂³×C₅	—	2	1	no	—
239	C₂³×C₅	—	3	1	no	—
240	C₂³×C₅	—	6	4	no	—
241	C₂³×C₅	—	6	1	no	—
242	C₂³×C₅	—	12	2	no	—
243	C₂³×C₅	—	12	2	no	—
244	C₅×D₄	—	2	1	no	—
245	C₅×D₄	—	3	2	no	—
246	C₅×D₄	—	6	4	no	—
247	C₅×D₄	—	6	1	no	—
248	C₅×D₄	D₃×C₈	1	2	yes	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	3	1	no	—
251	C₂×C₄×C₅	—	3	2	no	—
252	C₂×C₄×C₅	—	3	2	no	—
253	C₂×C₄×C₅	—	3	1	no	—
254	C₂×C₄×C₅	—	3	1	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	6	1	no	—
258	C₂×C₄×C₅	—	6	1	no	—
259	C₂×C₄×C₅	—	6	1	no	—
260	C₂×C₄×C₅	—	12	1	no	—
261	C₂×C₄×C₅	—	12	2	no	—
262	C₂×C₄×C₅	—	12	2	no	—
263	C₂×C₄×C₅	—	12	2	no	—
264	C₂×C₄×C₅	—	12	1	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
269	C₅×C₈	—	4	1	no	—
270	C₅×C₈	—	4	1	no	—
271	C₅×C₈	—	12	1	no	—
272	C₅×C₈	—	12	1	no	—
273	C₂²×D₄	—	3	1	no	—
274	C₂³×C₄	—	6	1	no	—
275	C₄×D₄	—	3	1	no	—
276	C₄×D₄	—	3	1	no	—
277	C₄×D₄	—	3	1	no	—
278	C₄×D₄	—	6	1	no	—
279	C₄×D₄	—	6	1	no	—
280	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₂²⋊C₄	—	6	1	no	—
283	C₂×C₄²	—	3	1	no	—
284	C₄⋊C₈	—	3	1	no	—
285	C₄⋊C₈	—	6	1	no	—
286	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
287	C₂²⋊C₈	—	6	1	no	—
288	C₂²⋊C₈	—	6	1	no	—
289	C₄×C₈	—	3	1	no	—
290	C₄×C₈	—	6	1	no	—
291	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
292	C₂×C₃×C₅	—	4	2	no	—
293	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
294	C₂×C₃×C₅	#418	1	1	yes	characteristic
295	C₂×C₃×C₅	#421	1	1	yes	characteristic
296	C₅×D₃	—	2	2	no	—
297	C₅×D₃	—	4	2	no	—
298	C₂³×C₃	—	2	1	no	—
299	C₂²×D₃	—	2	1	no	—
300	C₂²×D₃	—	2	4	no	—
301	C₂²×D₃	—	4	2	no	—
302	C₂²×D₃	—	4	2	no	—
303	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
304	C₃×D₄	—	2	1	no	—
305	C₃×D₄	C₂×C₅×C₈	1	2	yes	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	#67	—	2	4	no	—
313	C₂×Dic₃	—	2	1	no	—
314	C₂×Dic₃	—	4	2	no	—
315	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
318	D₁₂	—	2	1	no	—
319	D₁₂	C₂×C₅×C₈	1	2	yes	—
320	C₄×D₃	—	2	1	no	—
321	C₄×D₃	—	2	1	no	—
322	C₄×D₃	—	4	1	no	—
323	C₄×D₃	—	4	2	no	—
324	C₄×D₃	—	4	2	no	—
325	C₄×D₃	—	4	1	no	—
326	C₄×D₃	—	4	1	no	—
327	C₄×D₃	C₂×C₅×C₈	1	2	yes	—
328	C₄×D₃	C₅×M₁₆	1	2	yes	—
329	C₃×C₈	—	4	1	no	—
330	C₃×C₈	—	4	1	no	—
331	C₃⋊C₈	—	4	1	no	—
332	C₃⋊C₈	—	4	1	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	3	2	no	—
335	C₂²×C₅	—	4	1	no	—
336	C₂²×C₅	—	4	1	no	—
337	C₂²×C₅	—	6	1	no	—
338	C₂²×C₅	—	6	1	no	—
339	C₂²×C₅	—	6	2	no	—
340	C₂²×C₅	—	12	8	no	—
341	C₂²×C₅	—	12	1	no	—
342	C₂²×C₅	—	12	1	no	—
343	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	—	3	2	no	—
346	C₄×C₅	—	4	1	no	—
347	C₄×C₅	—	6	1	no	—
348	C₄×C₅	—	6	1	no	—
349	C₄×C₅	—	12	1	no	—
350	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
351	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
352	C₄×C₅	#911	1	1	yes	characteristic
353	C₄×C₅	#914	1	1	yes	characteristic
354	C₂⁴	—	6	1	no	—
355	C₂×D₄	—	3	4	no	—
356	C₂×D₄	—	3	1	no	—
357	C₂×D₄	—	6	2	no	—
358	C₂×D₄	—	6	1	no	—
359	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	3	1	no	—
362	C₂²×C₄	—	3	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	6	1	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	6	1	no	—
368	C₂²×C₄	—	12	2	no	—
369	C₂²×C₄	—	12	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	6	1	no	—
373	C₂×C₈	—	6	1	no	—
374	C₄⋊C₄	—	3	1	no	—
375	C₄⋊C₄	—	6	1	no	—
376	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	6	1	no	—
379	C₂²⋊C₄	—	6	1	no	—
380	C₂²⋊C₄	—	6	1	no	—
381	C₄²	—	3	1	no	—
382	C₄²	—	3	1	no	—
383	C₄²	—	3	1	no	—
384	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
385	C₃×C₅	#1478	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	4	1	no	—
388	C₂²×C₃	—	4	1	no	—
389	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×D₃	—	2	1	no	—
391	C₂×D₃	—	2	1	no	—
392	C₂×D₃	—	2	2	no	—
393	C₂×D₃	—	4	8	no	—
394	C₂×D₃	—	4	1	no	—
395	C₂×D₃	—	4	1	no	—
396	C₂×D₃	C₅×C₂²⋊C₈	1	2	yes	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	4	1	no	—
399	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
400	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
401	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
403	Dic₃	—	2	1	no	—
404	Dic₃	—	2	1	no	—
405	Dic₃	—	4	1	no	—
406	Dic₃	C₅×C₂²⋊C₈	1	2	yes	—
407	C₂×C₅	—	4	2	no	—
408	C₂×C₅	—	6	2	no	—
409	C₂×C₅	—	12	2	no	—
410	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
411	C₂×C₅	#4770	1	1	yes	characteristic
412	C₂×C₅	#4821	1	1	yes	characteristic
413	C₂³	—	2	1	no	—
414	C₂³	—	3	1	no	—
415	C₂³	—	6	4	no	—
416	C₂³	—	6	1	no	—
417	C₂³	—	12	2	no	—
418	C₂³	—	12	2	no	—
419	D₄	—	2	1	no	—
420	D₄	—	3	2	no	—
421	D₄	—	6	4	no	—
422	D₄	—	6	1	no	—
423	D₄	C₅×D₃×C₈	1	2	yes	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	3	1	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	6	1	no	—
433	C₂×C₄	—	6	1	no	—
434	C₂×C₄	—	6	1	no	—
435	C₂×C₄	—	12	1	no	—
436	C₂×C₄	—	12	2	no	—
437	C₂×C₄	—	12	2	no	—
438	C₂×C₄	—	12	2	no	—
439	C₂×C₄	—	12	1	no	—
440	C₂×C₄	—	12	1	no	—
441	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
442	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
443	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	12	1	no	—
447	C₈	—	12	1	no	—
448	C₂×C₃	—	4	2	no	—
449	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
450	C₂×C₃	C₅×#418	1	1	yes	characteristic
451	C₂×C₃	C₅×#421	1	1	yes	characteristic
452	D₃	—	2	2	no	—
453	D₃	—	4	2	no	—
454	C₅	#68167	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	2	2	no	—
456	C₂²	—	3	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	6	1	no	—
460	C₂²	—	6	1	no	—
461	C₂²	—	6	2	no	—
462	C₂²	—	12	8	no	—
463	C₂²	—	12	1	no	—
464	C₂²	—	12	1	no	—
465	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	3	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	6	1	no	—
470	C₄	—	6	1	no	—
471	C₄	—	12	1	no	—
472	C₄	C₂×C₅×D₃×C₈	1	1	yes	characteristic
473	C₄	C₅×D₃×M₁₆	1	1	yes	characteristic
474	C₄	C₅×#911	1	1	yes	characteristic
475	C₄	C₅×#914	1	1	yes	characteristic
476	C₃	C₅×#1478	1	1	yes	characteristic, complemented, Sylow
477	C₂	—	4	2	no	—
478	C₂	—	6	2	no	—
479	C₂	—	12	2	no	—
480	C₂	C₅×D₃×C₂²⋊C₈	1	1	yes	characteristic
481	C₂	C₅×#4770	1	1	yes	characteristic
482	C₂	C₅×#4821	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×D₄⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×D₃×D₄	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×D₄⋊C₈	D₃
hypocenter	C₃	C₅×#1478
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅ ◁ C₅×D₄⋊C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×#4833	C₂	semidirect
3. C₅×#4685	C₂	semidirect
4. C₃×C₅×D₄⋊C₈	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4483	C₂	semidirect
7. C₅×#4459	C₂	semidirect
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
21. C₃×C₄×C₅×C₈	C₂²	semidirect
26. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
27. C₄×C₅×C₃⋊C₈	C₂²	semidirect
28. #68167	C₅	direct (N × H)
35. C₅×D₄⋊C₈	D₃	semidirect
42. C₅×D₃×D₄	C₈	semidirect
68. #4833	C₂×C₅	semidirect
69. #4685	C₂×C₅	semidirect
70. C₃×D₄⋊C₈	C₂×C₅	semidirect
71. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
72. #4483	C₂×C₅	semidirect
73. #4459	C₂×C₅	semidirect
87. C₅×C₄⋊C₈	C₂×D₃	semidirect
92. C₄×C₅×C₈	C₂×D₃	semidirect
140. C₃×C₄⋊C₈	C₂²×C₅	semidirect
141. C₃×C₄×C₈	C₂²×C₅	semidirect
146. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
147. C₄×C₃⋊C₈	C₂²×C₅	semidirect
185. D₄⋊C₈	C₅×D₃	semidirect
213. D₃×D₄	C₅×C₈	semidirect
286. C₄⋊C₈	C₂×C₅×D₃	semidirect
291. C₄×C₈	C₂×C₅×D₃	semidirect
385. C₃×C₅	#1478	semidirect
454. C₅	#68167	direct (N × H)
476. C₃	C₅×#1478	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₅×D₃×D₄	2
C₅×#4833	2
C₅×#4685	2
C₃×C₅×D₄⋊C₈	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#4483	2
C₅×#4459	2
C₅×#1478	3
#68167	5

Subgroups — C5×#68167 #14281680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68167 #14281680